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Fluid simulation of the bias effect in inductive/capacitive dischargesYu-Ru Zhang, Fei Gao, Xue-Chun Li, Annemie Bogaerts, and You-Nian Wang Citation: Journal of Vacuum Science & Technology A 33, 061303 (2015); doi: 10.1116/1.4928033 View online: http://dx.doi.org/10.1116/1.4928033 View Table of Contents: http://scitation.aip.org/content/avs/journal/jvsta/33/6?ver=pdfcov Published by the AVS: Science & Technology of Materials, Interfaces, and Processing Articles you may be interested in Particle-in-cell simulations of hollow cathode enhanced capacitively coupled radio frequency discharges Phys. Plasmas 19, 023508 (2012); 10.1063/1.3685709 Phase-shift effects on growth and transport of dust particles in VHF capacitively coupled silane discharges: Twodimensional fluid simulation Phys. Plasmas 18, 083508 (2011); 10.1063/1.3626544 Verification of collisionless sheath model of capacitive rf discharges by particle-in-cell simulations J. Appl. Phys. 110, 033307 (2011); 10.1063/1.3620983 Comparison of atmospheric-pressure helium and argon plasmas generated by capacitively coupled radio-frequency discharge Phys. Plasmas 13, 093503 (2006); 10.1063/1.2355428 Modeling of ionization of argon in an analytical capacitively coupled radio-frequency glow discharge J. Appl. Phys. 86, 2990 (1999); 10.1063/1.371159

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Fluid simulation of the bias effect in inductive/capacitive discharges

Yu-Ru ZhangKey Laboratory of Materials Modification by Laser, Ion, and Electron Beams (Ministry of Education),School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024,China and Research Group PLASMANT, Department of Chemistry, University of Antwerp,Universiteitsplein 1, Wilrijk, BE-2610 Antwerp, Belgium

Fei Gao and Xue-Chun LiKey Laboratory of Materials Modification by Laser, Ion, and Electron Beams (Ministry of Education),School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024, China

Annemie BogaertsResearch Group PLASMANT, Department of Chemistry, University of Antwerp, Universiteitsplein 1, Wilrijk,BE-2610 Antwerp, Belgium

You-Nian Wanga)

Key Laboratory of Materials Modification by Laser, Ion, and Electron Beams (Ministry of Education),School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024, China

(Received 16 April 2015; accepted 24 July 2015; published 7 August 2015)

Computer simulations are performed for an argon inductively coupled plasma (ICP) with a

capacitive radio-frequency bias power, to investigate the bias effect on the discharge mode transi-

tion and on the plasma characteristics at various ICP currents, bias voltages, and bias frequencies.

When the bias frequency is fixed at 13.56 MHz and the ICP current is low, e.g., 6 A, the spatiotem-

poral averaged plasma density increases monotonically with bias voltage, and the bias effect is al-

ready prominent at a bias voltage of 90 V. The maximum of the ionization rate moves toward the

bottom electrode, which indicates clearly the discharge mode transition in inductive/capacitive dis-

charges. At higher ICP currents, i.e., 11 and 13 A, the plasma density decreases first and then

increases with bias voltage, due to the competing mechanisms between the ion acceleration power

dissipation and the capacitive power deposition. At 11 A, the bias effect is still important, but it is

noticeable only at higher bias voltages. At 13 A, the ionization rate is characterized by a maximum

at the reactor center near the dielectric window at all selected bias voltages, which indicates that

the ICP power, instead of the bias power, plays a dominant role under this condition, and no mode

transition is observed. Indeed, the ratio of the bias power to the total power is lower than 0.4 over a

wide range of bias voltages, i.e., 0–300 V. Besides the effect of ICP current, also the effect of vari-

ous bias frequencies is investigated. It is found that the modulation of the bias power to the spatio-

temporal distributions of the ionization rate at 2 MHz is strikingly different from the behavior

observed at higher bias frequencies. Furthermore, the minimum of the plasma density appears at

different bias voltages, i.e., 120 V at 2 MHz and 90 V at 27.12 MHz. VC 2015 American Vacuum Society.[http://dx.doi.org/10.1116/1.4928033]

I. INTRODUCTION

Inductively coupled plasma (ICP) sources are being

widely used in the semiconductor manufacturing industry, as

they are characterized by several advantages, such as high

plasma density at low gas pressure, relative simplicity, no

requirement for external magnetic fields, and so on.1,2 For

etching and deposition processes, it is important to control

the plasma density and ion bombardment energy independ-

ently, which is difficult to be realized in purely inductive dis-

charges. Therefore, a radio-frequency (RF) bias power is

often employed and capacitively coupled to the substrate.3–7

In this discharge system, the plasma is generated by the ICP

power, which controls the plasma density and ion flux, and

the capacitive bias power is used to control the energy of the

ions at the substrate. The bias power, which determines the

ion energy distribution (IED) at the wafer, has a significant

influence on the plasma properties and is, for instance, re-

sponsible for the etch rate. Hence, the bias power effect

should be systematically investigated, in order to control the

discharge process and to optimize the plasma for microelec-

tronics applications.

In recent years, significant progress has been achieved in

experimental studies of the bias effect in inductive dis-

charges with a biased electrode.8–13 Rauf et al.8 measuredthe electron density and total negative ion density in Ar/SF6plasmas, by using microwave interferometry and laser pho-

todetachment, respectively. Sobolewski and Kim9 performed

measurements with a cutoff probe and a Langmuir probe,

and reported a bias-induced decrease in the electron density

at high ICP powers in Ar, CF4, and Ar/CF4 plasmas.

However, when the ICP power is low, a strikingly different

evolution was observed, and the RF bias produced an

increase in the electron density. Lee et al.10 revealed that theplasma density increased considerably with bias power when

the discharge was in capacitive mode (E mode), whereas aa)Electronic mail: [email protected]

061303-1 J. Vac. Sci. Technol. A 33(6), Nov/Dec 2015 0734-2101/2015/33(6)/061303/13/$30.00 VC 2015 American Vacuum Society 061303-1


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decreasing trend was observed in the inductive mode (H

mode), which was in good agreement with the experimental

results presented in Ref. 9. Last year, Schulze et al.11 veri-fied experimentally, by phase resolved optical emission

spectroscopy as well as current and voltage measurements,

that three coupling mechanisms (i.e., sheath heating due to

the bias power, the substrate sheath voltage affected by the

ICP power, and the amplitude as well as the frequency of

plasma series resonance oscillations of the RF current

affected by the ICP power) were potentially limiting the sep-

arate control of the ion energy and flux in a neon ICP dis-

charge with RF bias. Subsequently, Lee et al.12 performedmeasurements in an ICP reactor with bias frequency of 12.5

MHz and came to the conclusion that the plasma density

near the radial edge had a pronounced increase, and there-

fore, the plasma uniformity was improved significantly when

a bias power was applied. Furthermore, Lee and Chung13

discovered that the high energy electrons were generated by

the capacitively coupled collisionless heating of the electron

bounce resonance, when a high RF bias power was coupled

to the substrate.

In addition, some theoretical research has also been put

forward to investigate the bias effect in a combined plasma

reactor with both ICP power and RF bias.8,14–19 Rauf et al.8

employed the hybrid plasma equipment model (HPEM) with

a detailed plasma chemistry description and showed that the

RF bias power had very little effect on the ion and electron

densities in an Ar/SF6 discharge. Hoekstra and Kushner14

focused on the IED by using the HPEM coupled with the

plasma chemistry Monte Carlo simulation module. They dis-

covered that the shape of the IED depends both on the ampli-

tude of the RF bias (which determines the average energy of

the IED) and on the ICP power (which determines the width

of the IED). Takekida and Nanbu15 utilized a particle-in cell

Monte Carlo method, showing that the uniformity of the ion

flux could be improved by decreasing the bias frequency.

Tinck et al.16 illustrated with the HPEM that the energy andfluxes of the ions hitting the substrate became higher at

increasing bias, and this gave rise to a higher etch rate.

Kwon et al.17 presented a self-consistent global model com-bined with a sheath module to examine the bias power effect

on the plasma properties. Finally, Zhang and Kushner18 and

Rauf19 investigated the influence of the bias power on the

etch rate in C2F6 and CF4/O2 plasmas, respectively.

Indeed, the bias power can penetrate into the plasma bulk,

contribute to the electron heating, and therefore change the

plasma characteristics. From the literature overview men-

tioned above, it is clear that quite a lot of research has been

carried out already on the bias effect in ICP discharges, but

there still remain some questions, especially regarding the

effect on the discharge mode transition. In the previous

investigations, the emphasis was mainly put on the IED

(Refs. 14–16) and etch rate18,19 in the ICP reactor with a bi-

ased substrate. Although the plasma density has been

reported as a function of bias power in Refs. 8 and 17, the

qualitative trend was not in good agreement with the experi-

mental results observed in Ref. 13, and the mechanisms

behind the bias effect are still not clear. When a capacitive rf

bias is applied to the substrate, an rf voltage drop is produced

at the boundary of the plasma, and the plasma potential will

be modulated. Moreover, the electrons can be heated not

only by the inductive power, but also by the rf sheath oscilla-

tion, and hence, the balance between the power absorption

and power dissipation will be changed, and this has a direct

influence on the plasma properties. In order to obtain optimal

device performance during the etching process, the plasma

parameters must be carefully controlled, so it is of great im-

portance to elucidate the bias effect on the plasma character-

istics. Therefore, a comprehensive, detailed study of the bias

effect on the discharge mode transition and on the plasma

properties, especially under different discharge conditions,

should be carried out. In this paper, the so-called

Multiphysics Analysis for Plasma Sources-ICP (MAPS-ICP)

solver25 accompanied with the MAPS-sheath module35 has

been employed, to investigate the bias effect on the dis-

charge mode transition and plasma characteristics in an ICP

reactor at various ICP currents, bias voltages, and bias fre-

quencies. Indeed, it is very important to have a good insight

in the bias effect, because it has a significant influence on the

plasma properties and plays a key role in plasma processing

applications.

II. DESCRIPTION OF THE FLUID MODEL

A schematic of the ICP reactor with capacitively coupled

bias power, studied in this work, is shown in Fig. 1. The re-

actor is cylindrical, with a radius of 15 cm. The discharge is

sustained by a two-turn planar coil, which is separated from

the plasma by a dielectric window. The radii of the inner and

outer turns of the coil are 6 and 8 cm, respectively. The bot-

tom electrode with a radius of 13 cm is fixed at a distance of

9 cm from the quartz window and is biased by a RF power to

independently control the ion bombardment energy.

MAPS is a comprehensive modeling platform developed

by Prof. Wang and his group for the multiphysics analysis of

various plasma sources. It consists of a series of modules,

FIG. 1. Schematic picture of the cylindrical inductively coupled plasma reac-

tor configuration.

061303-2 Zhang et al.: Fluid simulation of the bias effect in inductive/capacitive discharges 061303-2

J. Vac. Sci. Technol. A, Vol. 33, No. 6, Nov/Dec 2015


which are iterated to reach a converged solution. MAPS

includes two solvers: the MAPS-CCP solver and the MAPS-

ICP solver. The MAPS-CCP solver, which is used to investi-

gate the multiphysical coupling phenomena in capacitively

coupled discharges, is composed of a two-dimensional fluid

model20,21 and a particle-in-cell/Monte Carlo method.22,23

For the MAPS-ICP solver, only the two-dimensional fluid

model is employed,,24,25 focusing on the discharge proper-

ties in inductively coupled plasmas. To complete the MAPS,

some other modules are also included, for instance, the input

module, the output module, the reaction chemistry module,

the electromagnetic module, and the sheath module. The

MAPS-sheath module can be used to describe the spatiotem-

poral characteristics of the RF sheath. Except for the mod-

ules mentioned above, other functions of the MAPS are

currently under development.

In this paper, the MAPS-ICP solver combined with the

MAPS-sheath module is employed to investigate the bias

effect on the discharge mode transition and plasma charac-

teristics in a combined discharge with both inductive and

bias powers. The modules are described as follows.

A. Input module

Before we start the simulation, the discharge parameters

and the reactor geometry should be defined as input in the

model. The discharge parameters consist of three parts:

source parameters, gas parameters, and numerical treatment

parameters. In the source parameter part, the amplitudes and

frequencies of the ICP power and RF bias are defined, as

well as the phase shift value between them. Subsequently,

the type of gas, gas pressure, and gas mixing ratio are chosen

in the gas parameter section. Finally, numerical treatment

parameters, which are responsible for the accuracy, stability,

and efficiency of the numerical simulation, should also be

given as input. These parameters include initial values of the

plasma properties (i.e., the plasma density, electron tempera-

ture, and so on), the time step, and iteration factors of suc-

cessive-over-relaxation (SOR), and other algorithms.

In addition, the reactor geometry is also an important

input factor in the simulation. It includes the dimensions of

the electrode and the discharge region, the relative dielectric

constant of the dielectric window, and the position of the

coil. Besides, the boundary conditions, which include the

axis boundary, source boundary, grounded boundary,

dielectric boundary, and outflow boundary, must be specified

in order to complete the problem.

B. Reaction chemistry module

There exist various kinds of plasma species in the dis-

charge, including molecules, radicals, positive and negative

ions, excited species, as well as electrons. These species react

with each other in a large number of collisions, and therefore,

a list of all the important chemical reactions is constructed in

the reaction chemistry module, including electron-impact

(electron-neutral and electron-ion) collisions and heavy parti-

cle (i.e., ion–ion, ion–neutral, and neutral– neutral) reactions.

For all these reactions, energy-dependent cross sections (for

the electron-impact collisions) and rate coefficients (for the

heavy particle reactions) are collected, and are used as input

into the source terms, which will be used for solving the conti-

nuity equations. Besides, the transport coefficients (i.e., diffu-

sion coefficients for the plasma species, as well as the

viscosity and the thermal conductivity for a pure gas or gas

mixtures) are also defined in this module.

In this work, the simulations were performed for an Ar

plasma, and the species considered in the model include the

electrons, Arþ, and Ar*. All the reactions taken into account

in the model are presented in Table I.

C. Plasma module

In the plasma module, which forms the core of the

MAPS-ICP solver, the plasma is treated as a continuum,

which consists of a large number of plasma species, includ-

ing various molecules, radicals, ions, excited species, as well

as electrons. The average quantities of these particles, such

as density, mean velocity, and mean energy, can be obtained

by solving the moments of the Boltzmann equation, which

are formed by multiplying the Boltzmann equation by

v0; v1; v2, and integrating over velocity.We solve the equations of continuity and energy for

electrons

@ne@tþr � Ce ¼ Se; (1)

@3

2nekBTe

� �

@t¼ �r � qe � eEs � Ce þ Pind �We; (2)

TABLE I. Chemical reactions included in the model.

Process Reaction Rate coefficient (cm3/s) References

Ground state ionization eþAr! 2eþArþ a 36Ground state excitation eþAr! eþAr* a 37b

Stepwise ionization eþAr*! 2eþArþ a 38b

Superelastic collision eþAr*! eþAr a 39b

Quenching to resonant; radiative decay eþAr*! eþAr 2.0� 10�7 40b

Metastable pooling Ar*þAr*! eþArþþAr 6.2� 10�10 40b

Two-body quenching ArþAr*! 2Ar 3.0� 10�15 40b

aThe rate coefficient is calculated from the corresponding collision cross section.bAr* represents a composite metastable level consisting of 3P0 and

3P2.


JVST A - Vacuum, Surfaces, and Films


where the electron flux Ce can be presented in the drift-diffusion form

Ce ¼ �1

me�enr nekBTeð Þ �

eneme�en

Es; (3)

and the flux of energy qe is expressed as

qe ¼5

2kBTeCe �

5

2

nekBTeme�en

r kBTeð Þ: (4)

Here, ne, me, and Te are the density, mass, and temperature ofthe electrons, respectively; Es is the static electric field; �en isthe collision frequency between electrons and neutral par-

ticles; kB is the Boltzmann constant; Se is the source of elec-trons; We ¼

Pj ejkjn1n2 is the energy exchange during all the

collisional processes; and kj is the reaction coefficient.Positive values of ej imply energy loss by electrons (e.g., ioni-zation), and negative values imply energy gain (e.g., supere-

lastic collisions). The period averaged inductive heating term

Pind is described as Pind ¼ 1=TÐ T

0JhEhdt.

The behavior of the ions is governed by the continuity

equation and momentum balance equation. Since the ions

are assumed to be at room temperature, no energy balance

equation needs to be solved for them

@ni@tþr � niuið Þ ¼ Si; (5)

@ nimiuið Þ@t

þr � nimiuiuið Þ ¼ �rpi þ ZieniEs þMi:

(6)

Here, ni, ui, Si, mi, and Zi are the ion density, velocity, sourceterm, mass, and charge, respectively; pi is the ion pressure;and Mi represents the collisional transfer of momentumfrom ions to neutral species.26

The electrostatic fields due to the space charge within the

plasma, which in turn influence the charged particle behav-

ior, can be determined by solving the Poisson’s equation

r2/ ¼ ee0

ne �X

Zþnþ þX

Z�n�

� �; (7)

where / is the electric potential and e0 is the vacuumpermittivity.

The electron flux at the electrodes and side walls is given

by using the kinetically limited Maxwellian flux condition

Ce ¼ 61=4neue;th expð/b=kBTeÞ, where the 6 signs corre-spond to the direction of the electron flux, /b is the boundarypotential, and ue;th is the electron thermal velocity, expressed

as ue;th ¼ ð8kBTe=pmeÞ1=2. Electron reflection at the bounda-ries is accounted for, with a reflection coefficient H of 0.25.Ignoring the electron thermal conduction, the energy flux to

the electrodes and walls is set to qe ¼ 5=2kBTeCe. The iondensity and velocity gradients are set to zero at the bounda-

ries, i.e., rni¼ 0 and r � ui ¼ 0.At the top dielectric surface, the boundary condition for

the electric potential / is given by27

/ ¼ /1 þ Dz rs=e0 þ ed/2=e0=Lð Þ1þ Dzed=e0=L

: (8)

Here, /1 is the plasma potential at a distance Dz from thedielectric surface, and /2 is the potential on the oppositeside of the dielectric from the plasma; rs is the surfacecharge density; and ed and L are the permittivity and thick-ness of the dielectric region, respectively.

D. Electromagnetic module

In ICP discharges, the plasma is generated by the induc-

tively coupled electric fields, which are governed by the

Maxwell equations

r� E ¼ � @B@t; (9)

r� B ¼ l0Jþ l0e0er@E

@t; (10)

where E and B are the time-varying electric field and mag-netic field; l0 and er are the vacuum permeability and the rel-ative dielectric constant of the quartz window, respectively.

The plasma current in the discharge region is given by

@J

@t¼ e

2neme

E� �enJ: (11)

However, in the vacuum region and dielectric region, the

plasma current J equals zero.Based on the boundary conditions for the electromagnetic

fields at the material interface n� ðE2 � E1Þ ¼ 0 andn� ðB2 � B1Þ ¼ l0a, both the azimuthal component of theelectric field Eh and the radial component of the magneticfield Br are continuous at the interface of the plasma regionand the dielectric window. However, at the interface of the

dielectric window and the vacuum region, where the coil set

is placed, Ehjvac ¼ Ehjdie and Brjvac � Brjdie ¼ l0ah, whereah is the current density.

E. Sheath module

In order to accurately investigate the bias effect on the

plasma characteristics under various discharge conditions, a

sheath module should be included in the MAPS-ICP solver.

Over the past few years, the behavior of the sheath has been

studied by various sheath models.28–35 In this paper, we

assume that the sheath is uniform in the radial direction. This

is justified because, although the electron density is not uni-

form in the radial direction, the absolute value in the sheath

only has a 20% drop from the center to the radial edge.

Moreover, only the axial components of the electron flux and

the ion flux are needed in the current balance equation to

solve for the potential at the electrode, as will be discussed

below. Therefore, in order to reduce the computational bur-

den, a self-consistent one-dimensional dynamic sheath model

is integrated into the two-dimensional MAPS-ICP solver.

More specifically, in the sheath, the spatiotemporal distribu-

tions of the charged particle density and flux, as well as of the

electric potential, are obtained by solving equations (1) and




(5)–(7) in the axial direction. The plasma properties at the

bulk-sheath interface calculated in the inductive plasma mod-

ule are used as the boundary conditions in the capacitive

sheath module.

The instantaneous voltage on the substrate depends not

only on the applied bias power but also on the transient

behavior of the sheath. Therefore, an equivalent circuit

model has been presented,33,35 in which the sheath is treated

as a parallel combination of a diode, a capacitor, and a cur-

rent source. Assuming that the current applied at the elec-

trode from the bias power is sinusoidal, the current balance

equation is given by

Ii � Ie � Id ¼ Imax sinð2pftÞ: (12)

Here, Imax and f are the amplitude and frequency of the biascurrent. Ii ¼ eð

PZþnþuþ �

PZ�n�u�ÞA is the ion cur-

rent, Ie¼ eneueA is the electron current at the electrode, andA is the surface area of the electrode. The displacement cur-rent Id can be derived as

Id ¼ CsdVedtþ Ve

dCsdt

; (13)

where Cs¼ e0 A/ds is the sheath capacitance, and ds is thesheath thickness. The potential at the electrode Ve is obtainedas output of the above current balance equation and is used

as the boundary condition in the inductive plasma module

above, when solving the Poisson equation. From the current

balance equation, it is clear that the potential at the electrode

Ve depends not only on the applied bias power but also onthe behavior of the electrons and ions in the sheath, as well

as the movement of the sheath. Therefore, the sheath dynam-

ics has an influence on the potential at the electrode and

accordingly affects the plasma properties in the bulk region.

Based on the variation of Ve as a function of time during oneRF cycle, the bias voltage is self-consistently calculated.

III. RESULTS AND DISCUSSION

A. Bias effect at different coil currents

The influence of the bias effect on the discharge mode

transition and plasma characteristics in an ICP reactor is

investigated at different coil currents (i.e., 6, 11, and 13 A).

The simulations were performed at a pressure of 20 mTorr at

various bias voltages in the range of 0–300 V. In the simula-

tion, the secondary electron emission coefficient is assumed

to be 0.1. Since the collisionless heating and the stochastic

heating caused by the biased sheath oscillation can be

ignored when the pressure is not extremely low, the dis-

charge is mainly sustained by the Ohmic heating. The fre-

quencies of the coil set and of the bias power are fixed at

13.56 MHz.

The spatiotemporal averaged electron density and the ra-

tio of the absorbed bias power Pbias to the total power Ptotal(i.e., the sum of the power absorption from the coil current

and the bias source) are plotted in Fig. 2 as a function of bias

voltage at different ICP currents. It is clear that when the

ICP current is relatively low, i.e., 6 A, the electron density

increases monotonically with bias voltage, which agrees

well with experimental data.9,10 Indeed, at the low coil cur-

rent, the bias power plays a dominate role in the plasma gen-

eration. The inductive power absorption from the coil

current is about 11 W in the case without bias power, and it

increases to 58 W at 300 V, whereas the capacitive bias

power is 477 W under this condition. The ratio of Pbias to

Ptotal is indeed as high as 90% at the bias voltage of 300 V.

The absorbed bias power in the plasma increases signifi-

cantly with bias voltage, and therefore results in a higher

plasma density (i.e., around 1.6� 109 cm�3 when there is nobias power and 1.8� 1010 cm�3 at the bias voltage of300 V).

However, when the ICP current becomes higher, i.e., 11

and 13 A, the plasma density shows a strikingly different

trend with rising bias voltage. At the ICP current of 11 A, the

plasma density first exhibits a rapid decrease with bias volt-

age (i.e., from 4.3� 1010 cm�3 at 0 V to 9.4� 109 cm�3 at60 V), and subsequently, it increases to 6.1� 1010 cm�3 at300 V. Likewise, at an ICP current of 13 A, the electron den-

sity decreases slightly from 1.5� 1011 cm�3 at 0 V bias volt-age until 1.4� 1011 cm�3 at a bias voltage of 90 V, andsubsequently, it increases again to about 2.9� 1011 cm�3 at300 V bias voltage. This behavior is similar to that observed

in Ref. 13. Indeed, as the current in the coil set increases,

especially at 13 A, the discharge is mainly sustained by the

FIG. 2. (Color online) Evolutions of (a) the spatiotemporal averaged plasma

density, and (b) the ratio of the bias power to the total power, with bias volt-

age at various ICP currents, for an argon discharge sustained at 13.56 MHz.




inductive field. This can also be understood by examining

the ratio between Pbias and Ptotal in Fig. 2(b). At 13 A,

although the bias power is 501 W at 300 V, the inductive

power absorption increases from 499 W in the case without

bias source to 752 W at 300 V, and therefore, the ratio is

lower than 0.4 at all selected bias voltages with a fixed ICP

current of 13 A.

The initial drop in electron density when applying a bias

voltage in the case of 11 or 13 A ICP coil current can be

understood by considering a global model1,10

n0 ¼Ptotal

euB Aeff ;geT;g þ Aeff;seT;sð Þ: (14)

Here, Ptotal is the total power absorption, uB is the Bohm ve-locity, Aeff,g, Aeff,s, eT,g, and eT,s are the effective area for par-ticle loss and the total energy loss at the grounded wall and

the substrate, respectively. The total energy loss eT consistsof three parts: the collisional energy loss ec, the kineticenergy loss per electron ee, and per ion ei. In our simulations,the electron temperature shows little change with the bias

voltage, and so are ec and ee.1 Since ei is the sum of the ion

energy entering the sheath and the energy gained by the ion

as it traverses the sheath, ei at the substrate depends stronglyon the sheath voltage and is much higher than that at the

grounded wall. Therefore, the plasma density is approxi-

mately proportional to the ratio of the total power absorption

Ptotal to the kinetic energy lost per ion ei. When a small biasvoltage is applied, although the total power deposition

increases with bias voltage, the bias power dissipation

caused by the ion acceleration is more dominant,10,13 and

this gives rise to a considerable decrease in the plasma den-

sity. As the bias voltage increases further, the electrons gain

more energy from the higher capacitive bias power, and

therefore, these energetic electrons enhance the plasma

generation.

The bias effect on the discharge mode transition and on

the plasma characteristics at the ICP current of 6 A is appa-

rent from the spatial distributions of the plasma density in

Fig. 3. When there is no bias power applied on the substrate

[Fig. 3(a)], the discharge is sustained by the pure inductive

power, and the peak of the plasma density appears along the

reactor centerline (z¼ 8.5 cm). As the bias voltage increasesto 90 V (Pbias¼ 47 W), no significant effect on the density isdetected, except for the absolute values, which are nearly 3.5

times as high as obtained without bias power. At the bias

voltage of 300 V (Pbias¼ 477 W), as shown in Fig. 3(c), themaximum of the plasma density moves slightly toward the

bottom electrode with higher absolute values. This indicates

that the bias power has a dominant influence on the plasma

characteristics under this condition, and the electrons gain

more energy from the higher capacitive bias power, enhanc-

ing the ionization.

In order to understand the different plasma density profiles,

the spatial distributions of the ionization rate obtained at vari-

ous voltages are presented in Fig. 4. When the ICP current is

low (i.e., 6 A) without RF bias power [Fig. 4(a)], the electrons

are heated mainly by the inductive azimuthal electric field

induced by the coil current, and the maximum of the ioniza-

tion rate appears at the reactor center and close to the dielec-

tric window. The absolute value is very low, i.e., in the order

of 1.0� 1014 cm�3 s�1. As the bias voltage increases to 90 V,the electrons are heated not only by the inductive field but

also by the capacitive field caused by the RF bias. Therefore,

the electrons gain more energy from the bias power deposi-

tion, which gives rise to a considerable increase in the plasma

generation (leading to an ionization rate of 4.6� 1014 cm�3s�1), and the maximum of the ionization rate moves toward

the bottom electrode, as is clear from Fig. 4(b). Finally, when

a significant bias power is applied, corresponding to 300 V

[Fig. 4(c)], the discharge mode exhibits a transition. Indeed,

the discharge is mainly sustained by the capacitive bias

power, and accordingly, a prominent peak in the ionization

rate is observed along z¼ 8.5 cm, moving closer to the bottomelectrode at about r¼ 9 cm. Furthermore, the absolute value isone order of magnitude higher than that obtained in the case

without bias voltage.

FIG. 3. (Color online) Distributions of the plasma density at different bias

voltages: (a) 0 V, (b) 90 V, and (c) 300 V, for an argon discharge sustained

at an ICP current of 6 A and 13.56 MHz, with a bias frequency of 13.56

MHz.




When the ICP current increases to 11 and 13 A, the maxi-

mum of the plasma density becomes more intense and local-

ized at the reactor center at all selected bias voltages, and the

bias power has no significant influence on the distribution of

the plasma density, except for the absolute values (not shown

here). This is because the inductive coil power has a domi-

nant influence on the plasma characteristics, especially at

13 A.

When the ICP current increases to 11 A, the spatial distri-

butions of the ionization rate at various bias voltages are

strikingly different from those obtained at 6 A, both in shape

and especially in absolute values. When the bias voltage is

equal to 0, shown in Fig. 5(a), the ionization rate is charac-

terized by a remarkable peak at the reactor center near the

dielectric window. By comparing this with the results

obtained at the ICP current of 6 A, the ionization rate is more

localized with a higher absolute value, i.e., at a maximum

about 4.5� 1015 cm�3 s�1. As the bias voltage increases to90 V [Pbias¼ 57 W, see Fig. 5(b)], the RF bias power starts to

have an influence on the plasma properties, and the maximum

of the ionization rate moves away from the dielectric window,

which is similar to the result obtained in the low current case

[Fig. 4(b)]. As explained above, since more power dissipation

occurs due to the ion acceleration, the ionization rate dramati-

cally decreases to values of 1.1� 1015 cm�3 s�1. When thebias voltage increases further to 300 V (Pbias¼ 492 W), thepeak of the ionization rate appears almost along the reactor

centerline (z¼ 9 cm), and the absolute value becomes higheragain. Although more power is dissipated due to the ion accel-

eration as the bias voltage increases, the capacitive power

deposition induced by the RF bias has a predominant influ-

ence on the plasma production when the bias voltage is as

high as 300 V.

The evolution of ionization rate profiles with increasing

bias voltage at the ICP current of 13 A is depicted in Fig. 6.

It is clear that the ionization rate is localized at the reactor

center near the quartz window at all selected bias voltages,

which indicates that the RF bias power has no profound

FIG. 4. (Color online) Distributions of the ionization rate at different bias



MHz.




MHz.




influence on the plasma characteristics under these condi-

tions. This is because when the ICP current is relatively

high, the inductive field contributes significantly to the

plasma generation and is responsible for the spatial distribu-

tion of the ionization rate. In addition, the ionization rate first

slightly decreases, and then increases with rising bias volt-

age. This can again be explained by the competing mecha-

nisms between the power dissipation due to the ion

acceleration and the power absorption induced by the high

bias power.

To visualize the different bias effects at various ICP cur-

rents, the profiles of the ionization rate at r¼ 7 cm (i.e., in themiddle of the two-turns planar coil) are plotted in Figs. 7–9 as

a function of axial position and time within 1 RF cycle (1 RF

period¼ 74 ns). In a pure inductive discharge without RF biassource and at the coil current of 6 A [Fig. 7(a)], the electrons

are heated by the inductive field arising from the ICP current,

which is reflected by a substantial ionization in the bulk

region with two maxima during one period. Indeed, the

inductive field is first quite strong, therefore heating and

accelerating the electrons, which results in a large amount of

ionization (with a rate around 1.0� 1014 cm�3 s�1). At a latertime, the inductive field becomes weaker, but then it reverses,

and hence produces a second peak of the same magnitude.

Moreover, the ionization rate near the bottom electrode is con-

stant in time with a relatively low value, i.e., in the order of

2.5� 1013 cm�3 s�1. By switching on the bias source at 90 V[see Fig. 7(b)], the maximum of the ionization rate moves

downwards, explaining the result shown in Figs. 3(b) and

4(b). Besides, the ionization rate near the bottom electrode

becomes much more pronounced (i.e., around 2.0� 1014cm�3s�1), and it exhibits some fluctuation as a function of time.

This means that the influence of the capacitive power

becomes remarkable, and the discharge mode transition

occurs. When the bias voltage is equal to 300 V, only one

peak per RF cycle is observed instead of two, which appears

near the bottom electrode, and the maximum ionization rate is

much higher (i.e., almost 2.5� 1015cm�3 s�1). By comparing




MHz.

FIG. 7. (Color online) Spatiotemporal distributions of the ionization rate at r

¼ 7 cm at different bias voltages: (a) 0 V, (b) 90 V, and (c) 300 V, for an ar-gon discharge sustained at an ICP current of 6 A and 13.56 MHz, with a

bias frequency of 13.56 MHz.




with the ionization rate calculated without bias power, the dis-

charge is mainly sustained by the RF bias power under this

condition. A similar spatiotemporal distribution of the elec-

tron impact excitation rate has also been observed in neon

plasmas.11

The spatiotemporal distributions of the ionization rate at

different bias voltages with a fixed ICP current of 11 A are

presented in Fig. 8. When the bias source is switched off, the

ionization rate displays two peaks under the dielectric window

during one period, as is observed from Fig. 8(a). It is clear

that the peaks are more intense than those illustrated in

Fig. 7(a) (i.e., about 4.1� 1015 cm�3 s�1 versus about1.0� 1014 cm�3 s�1), because the heating is more localized athigher coil current. By switching on the bias source, a clear

difference can be observed, which indicates that the bias

power plays an important role in the plasma behavior. At the

bias voltage of 90 V, the two peaks become less prominent

with much lower values (i.e., around 1.0� 1015cm�3 s�1),

explaining the density decrease shown in Fig. 2(a). When the

bias voltage is as high as 300 V, the ionization rate becomes

higher again (i.e., 5.2� 1015cm�3 s�1), and the peaks movefurther downwards and appear at z¼ 10 cm, which is responsi-ble for the ionization rate profile with higher absolute values in

Fig. 5(c). Furthermore, the peak in the second half of the period

is more intense than that in the first half of the period. This

implies that the capacitive field has a significant influence on

the plasma production in this case. Besides, a minimum in the

ionization rate is detected near the biased electrode, and this

can again be attributed to the modulation of the bias power.

Finally, when the coil current is as high as 13 A (cf.

Fig. 9), the ionization rate is characterized by two peaks dur-

ing one period at all selected bias voltages, which gives rise

to a quite similar spatial distribution of the time-averaged

ionization rate in Fig. 6. By comparing with the results

obtained at lower ICP currents, it is clear that the maxima of

the ionization rate are more intense (around 1.3� 1016 cm�3










s�1 or higher) and more localized near the quartz window,

demonstrating that the inductive field plays a dominant role

under this condition. When there is no bias power, the ioni-

zation rate near the bottom electrode is constant in time, as

also observed in Fig. 8(a). As the bias voltage increases,

shown in Figs. 9(b) and 9(c), the ionization rate near the bot-

tom electrode exhibits some fluctuation as a function of

time, especially at the bias voltage of 300 V (Pbias¼ 501 W).This is again because the capacitive field acts in the opposite

direction at a later time within one RF cycle.

B. Bias effect at different bias frequencies

The bias effect on the discharge mode transition and

plasma characteristics does not only depend on the ICP cur-

rent, but also on the bias frequency. Therefore, in order to

completely understand the bias effect, the spatiotemporal

averaged plasma density, the ratio of Pbias to Ptotal, as well as

the distribution of the ionization rate are also calculated at

different bias frequencies (i.e., 2, 13.56, and 27.12 MHz),

with the ICP current fixed at 11 A. Under this condition, the

inductive power absorption is almost the same at different

bias frequencies, i.e., about 139 W at 0 V bias voltage, and

150 W at 300 V bias voltage.

It is clear from Fig. 10(a) that the spatiotemporal aver-

aged plasma density decreases first, and then increases with

rising bias voltage at all bias frequencies investigated, but

the minima appear at different bias voltages. Indeed, when

the bias frequency is 2 MHz, the minimum value appears at

a bias voltage of 120 V, whereas at 13.56 MHz and

27.12 MHz, the minima take place at a bias voltage of 60

and 90 V, respectively. This may be because when the bias

power and the coil current are at the same frequency, the

coupling efficiency of the two powers is higher than in the

other cases. Furthermore, at 2 MHz, the plasma density

exhibits only a slight increase with bias voltage (i.e., from

3.0� 1010 to 5.1� 1010 cm�3 at 2 MHz), whereas a morepronounced increase is observed at 13.56 and 27.12 MHz

(i.e., from 9.4� 109 to 6.1� 1010 cm�3 at 13.56 MHz, andfrom 1.9� 1010 to 7.0� 1010 cm�3 at 27.12 MHz). This indi-cates that the bias has a more significant influence on the

plasma characteristics at higher bias frequency. This is

because electrons gain more energy from the more frequent

collisions, and accordingly, they enhance the plasma genera-

tion. Besides, as the bias voltage increases, the ratio of Pbias

FIG. 10. (Color online) Evolutions of (a) the spatiotemporal averaged plasma

density, and (b) the ratio of the bias power to the total power, with bias volt-

age at various bias frequencies, for an argon discharge sustained at an ICP

current of 11 A and 13.56 MHz.


voltages: (a) 60 V, (b) 180 V, and (c) 300 V, for an argon discharge sus-

tained at an ICP current of 11 A and 13.56 MHz, with a bias frequency of 2

MHz.




to Ptotal increases significantly at all bias frequencies, but the

contribution of the bias power is somewhat lower at

27.12 MHz [cf. Fig. 10(b)]. This is again because of the

lower coupling efficiency of the two powers.

The spatial distributions of the ionization rate at different

bias voltages and a bias frequency of 2 MHz are plotted in

Fig. 11. When the bias electrode is grounded, the ionization

rate (not shown here) is the same as in Fig. 5(a), which is

characterized by a maximum at the center near the dielectric

window. When the bias source is switched on with a voltage

of 60 V (Pbias¼ 34 W) and 180 V (Pbias¼ 176 W), no signifi-cant effect on the ionization rate is detected, except for the

lower absolute values (i.e., 3.5� 1015 cm�3 s�1 at 60 V, and3.6� 1015 cm�3 s�1 at 180 V). As the bias voltage increasesto 300 V (Pbias¼ 334 W), the ionization rate becomes moreintense at the reactor center with higher absolute values, i.e.,

5.6� 1015 cm�3 s�1, as shown in Fig. 11(c).The effects of the bias power on the plasma characteris-

tics at a bias frequency of 27.12 MHz can be illustrated by

the ionization rate distributions depicted in Fig. 12. By com-

paring with the results obtained at low bias frequency, the

maxima of the ionization rate at 2 MHz are closer to the

dielectric window at all selected bias voltages. It is clear

from Fig. 12(a) that the maximum of the ionization rate

appears near the quartz window at about z¼ 10 cm when thebias voltage is 60 V (Pbias¼ 23 W). As the bias voltageincreases to 180 V and 300 V [Pbias¼ 136 and 278 W, seeFigs. 12(b) and 12(c)], the maximum moves toward the bot-

tom electrode and appears at about z¼ 9 cm at 300 V.Moreover, the ionization rate increases with the bias voltage,

and the absolute value, i.e., 5.8� 1015 cm�3 s�1 at 300 V, isa factor of 2.5 higher than that obtained at 60 V (around

2.3� 1015 cm�3 s�1).In order to understand the bias effect on the plasma tran-

sient behavior, the spatiotemporal distributions of the ioniza-

tion rate obtained at various voltages are presented for a bias

frequency of 2 MHz and 27.12 MHz in Figs. 13 and 14,


voltages: (a) 60 V, (b) 180 V, and (c) 300 V, for an argon discharge sus-

tained at an ICP current of 11 A and 13.56 MHz, with a bias frequency of

27.12 MHz.

FIG. 13. (Color online) Spatiotemporal distributions of the ionization rate at

r ¼ 7 cm at different bias voltages: (a) 60 V, (b) 180 V, and (c) 300 V, foran argon discharge sustained at an ICP current of 11 A and 13.56 MHz, with

a bias frequency of 2 MHz.




respectively. In Fig. 13, the results are plotted in a time-

frame of 500 ns, corresponding to one cycle at 2 MHz. At

this low bias frequency, the ionization primarily occurs

under the dielectric window at the bias voltage of 60 V and

is characterized by 14 peaks during one low frequency pe-

riod [cf. Fig. 13(a)], due to the energetic electrons acceler-

ated by the inductive field. As the bias voltage increases to

180 V [cf. Fig. 13(b)], the ionization is clearly modulated by

the bias effect, which is strikingly different from the results

obtained at 13.56 MHz. Indeed, the absolute values of the

peaks oscillate as a function of time, and a minimum of the

ionization rate appears near the bottom electrode, which

indicates that the bias power starts to have a significant influ-

ence on the plasma generation. At the bias voltage of 300 V,

shown in Fig. 13(c), the modulation of the bias power

becomes even more prominent. The peaks of the ionization

rate caused by the inductive field heating are first remarkable

at about 150 s (i.e., at maximum about 5.9� 1015 cm�3 s�1),

and at a later time they become less prominent (i.e., around

4.4� 1015 cm�3 s�1). Besides, the maximum of the ioniza-tion rate appears near the bottom electrode, which means

that the discharge is mainly sustained by the bias power

under this condition.

The comparison of the ionization rate profiles at various

bias voltages at the bias frequency of 27.12 MHz is depicted

in Fig. 14. During one low frequency period (74 ns for

13.56 MHz) at 60 V, the ionization is again at maximum

near the quartz window [Fig. 14(a)], which is similar to the

case at 13.56 MHz, 90 V [cf. Fig. 8(b)], except for the higher

absolute values (i.e., in the order of 2.2� 1015 cm�3 s�1). Atthe bias voltage of 180 and 300 V [see Figs. 14(b) and

14(c)], the maxima become more intense with higher abso-

lute values. Besides, the ionization rate exhibits two minima

above the bias electrode. This is because the RF capacitive

field induced by the bias power oscillates with time twice

within one low frequency cycle. Furthermore, it is clear that

the ionization rate distribution is different from that obtained

at the bias frequency of 13.56 MHz [Fig. 8(c)], which also

demonstrates the different modulation of the bias effect at

various frequencies.

IV. CONCLUSIONS

In this paper, the MAPS-ICP solver combined with the

MAPS-sheath module is employed to investigate the bias

effect on the discharge mode transition and plasma charac-

teristics in an argon inductively coupled plasma with a

capacitive bias power. The different effects at various ICP

currents, bias frequencies and bias voltages have been illus-

trated by examining the spatiotemporal averaged plasma

density, the ratio of the absorbed bias power to the total

power, as well as the distribution of the ionization rate.

From the simulation results, it is clear that the bias power

influences the mode transition and plasma properties in a dif-

ferent way at various coil currents. Indeed, when the current

is low, i.e., at 6 A, the spatiotemporal averaged plasma den-

sity increases monotonically with bias voltage, due to the

increasing bias power deposition. However, when the ICP

current becomes higher (i.e., 11 and 13 A), a strikingly dif-

ferent trend is observed. The plasma density decreases first

and then increases with bias voltage. This is because when

the bias voltage increases slightly, the power dissipation

caused by the ion acceleration becomes substantial and

therefore gives rise to a decrease in the plasma density.

However, as the bias voltage increases further, the power

deposition induced by the bias source plays a dominant role

in the plasma generation, and accordingly, it results in a

higher plasma density.

The spatial distribution of the ionization rate also exhibits

different profiles. When the bias source is switched off at the

ICP current of 6 A, the ionization rate has a broad maximum

at the reactor center near the dielectric window. As the bias

voltage increases, the peak moves toward the bottom elec-

trode with higher absolute values, which indicates the dis-

charge mode transition from inductive mode to capacitive

mode. As the current increases to 11 A without a bias source,

FIG. 14. (Color online) Spatiotemporal distributions of the ionization rate at

r ¼ 7 cm at different bias voltages: (a) 60 V, (b) 180 V, (c) 300 V, for an ar-gon discharge sustained at an ICP current of 11 A and 13.56 MHz, with a





the maximum under the quartz window is more intense and

more localized than that obtained at 6 A, and the absolute

value is higher. When the bias source is switched on, the

maximum of the ionization rate again moves downwards,

because of the pronounced capacitive bias power. At the

high coil current of 13 A, no significant effect of the bias

voltage on the ionization rate distribution is detected,

except for the absolute value, which indicates that the in-

ductive power plays a dominant role under this discharge

condition.

We also investigated the bias effect on the spatiotemporal

distribution of the ionization rate at r¼ 7 cm. When no biaspower is applied at 6 A, a substantial ionization takes place

in the bulk region with two peaks during one period. As the

bias voltage increases, the ionization rate displays only one

peak near the bottom electrode with higher values, which

means the discharge is mainly sustained in the capacitive

mode. However, when the ICP current increases to 11 A and

especially 13 A, the ionization rate is characterized by two

peaks under the dielectric window at all selected bias vol-

tages, which is typical for the inductive mode.

The different bias effects on the plasma characteristics

have also been demonstrated at various bias frequencies.

The evolution of the plasma density with bias voltage is sim-

ilar at all bias frequencies investigated, and is characterized

by first a drop and then a rise upon increasing bias voltage,

but the minimum appears at different bias voltages, i.e.,

120 V at 2 MHz, 60 V at 13.56 MHz, and 90 V at 27.12 MHz.

At the bias frequency of 2 MHz, the maxima of the ioniza-

tion rate are closer to the dielectric window than those

obtained at 27.12 MHz. Besides, the maxima of the ioniza-

tion rate oscillate as a function of time at 2 MHz, which indi-

cates the evident modulation of the bias effect.

ACKNOWLEDGMENTS

This work was supported by the Important National

Science and Technology Specific Project (Grant No.

2011ZX02403-001), the National Natural Science Foundation

of China (Grant Nos. 11175034, 11205025, and 11405019),

the China Postdoctoral Science Foundation (Grant No.

2014M561219), the Fundamental Research Funds for Central

Universities (Grant No. DUT14RC(3)071), the International

Science and Technology Cooperation Program of China

(Grant No. 2012DFG02150), the joint research project in the

framework of the agreement between MOST and FWO, and

the University of Antwerp BOF fellowship for Y.-R. Zhang.

1M. A. Lieberman and A. J. Lichtenberg, Principles of Plasma Dischargesand Materials Processing, 2nd ed. (Wiley, New York, 2005).

2P. L. G. Ventzek, M. Grapperhaus, and M. J. Kushner, J. Vac. Sci.

Technol., B 12, 3118 (1994).3J. H. Keller, J. C. Forster, and M. S. Barnes, J. Vac. Sci. Technol., A 11,2487 (1993).

4G. A. Hebner and P. A. Miller, J. Appl. Phys. 87, 7660 (2000).5D. S. Wuu, C. R. Chung, Y. H. Liu, R. H. Horng, and S. H. Huang, J. Vac.

Sci. Technol., B 20, 902 (2002).6N. O. V. Plank, M. A. Blauw, E. W. J. M. van der Drift, and R. Cheung,

J. Phys. D: Appl. Phys. 36, 482 (2003).7S. Imai, J. Vac. Sci. Technol., B 26, 2008 (2008).8S. Rauf, P. L. G. Ventzek, I. C. Abraham, G. A. Hebner, and J. R.

Woodworth, J. Appl. Phys. 92, 6998 (2002).9M. A. Sobolewski and J. H. Kim, J. Appl. Phys. 102, 113302 (2007).

10H. C. Lee, M. H. Lee, and C. W. Chung, Appl. Phys. Lett. 96, 071501 (2010).11J. Schulze, E. Schungel, and U. Czarnetzki, Appl. Phys. Lett. 100, 024102

(2012).12H. C. Lee, S. Oh, and C. W. Chung, Plasma Sources Sci. Technol. 21,

035003 (2012).13H. C. Lee and C. W. Chung, Appl. Phys. Lett. 101, 244104 (2012).14R. J. Hoekstra and M. J. Kushner, J. Appl. Phys. 79, 2275 (1996).15H. Takekida and K. Nanbu, J. Phys. D: Appl. Phys. 38, 3461 (2005).16S. Tinck, W. Boullart, and A. Bogaerts, J. Phys. D: Appl. Phys. 41,

065207 (2008).17D. C. Kwon, W. S. Shang, M. Park, D. H. You, M. Y. Song, S. J. You, Y.

H. Im, and J. S. Yoon, J. Appl. Phys. 109, 073311 (2011).18D. Zhang and M. J. Kushner, J. Vac. Sci. Technol., A 19, 524 (2001).19S. Rauf, J. Vac. Sci. Technol., B 22, 202 (2004).20Y. R. Zhang, X. Xu, S. X. Zhao, A. Bogaerts, and Y. N. Wang, Phys.

Plasmas 17, 113512 (2010).21Y. R. Zhang, A. Bogaerts, and Y. N. Wang, J. Phys. D: Appl. Phys. 45,

485204 (2012).22H. Y. Wang, W. Jiang, and Y. N. Wang, Plasma Sources Sci. Technol. 19,

045023 (2010).23W. Jiang, H. Y. Wang, Z. H. Bi, and Y. N. Wang, Plasma Sources Sci.

Technol. 20, 035013 (2011).24S. X. Zhao, X. Xu, X. C. Li, and Y. N. Wang, J. Appl. Phys. 105, 083306

(2009).25X. J. Si, S. X. Zhao, X. Xu, A. Bogaerts, and Y. N. Wang, Phys. Plasmas

18, 033504 (2011).26J. D. Bukowski, D. B. Graves, and P. Vitello, J. Appl. Phys. 80, 2614 (1996).27P. L. G. Ventzek, R. J. Hoekstra, and M. J. Kushner, J. Vac. Sci. Technol., B

12, 461 (1994).28M. A. Liberman, IEEE Trans. Plasma Sci. 16, 638 (1988).29V. A. Godyak and N. Sternberg, Phys. Rev. A 42, 2299 (1990).30M. J. Grapperhaus and M. J. Kushner, J. Appl. Phys. 81, 569 (1997).31P. A. Miller and M. E. Riley, J. Appl. Phys. 82, 3689 (1997).32T. Panagopoulos and D. J. Economou, J. Appl. Phys. 85, 3435 (1999).33E. A. Edekberg and E. S. Aydil, J. Appl. Phys. 86, 4799 (1999).34D. Bose, T. R. Govindan, and M. Meyyappan, J. Appl. Phys. 87, 7176 (2000).35Z. L. Dai, Y. N. Wang, and T. C. Ma, Phys. Rev. E 65, 036403 (2002).36D. Rapp and P. Englander-Golden, J. Chem. Phys. 43, 1464 (1965).37W. L. Morgan, “Kinema Research & Software,” http://www.lxcat.lapla-

ce.univ-tlse.fr/.38D. Ton-That and M. R. Flannery, Phys. Rev. A 15, 517 (1977).39F. Gao, S. X. Zhao, X. S. Li, and Y. N. Wang, Phys. Plasmas 16, 113502

(2009).40D. P. Lymberopoulos and D. J. Economou, J. Appl. Phys. 73, 3668 (1993).



http://dx.doi.org/10.1116/1.587488http://dx.doi.org/10.1116/1.587488http://dx.doi.org/10.1116/1.578597http://dx.doi.org/10.1063/1.373437http://dx.doi.org/10.1116/1.1475983http://dx.doi.org/10.1116/1.1475983http://dx.doi.org/10.1088/0022-3727/36/5/310http://dx.doi.org/10.1116/1.3021031http://dx.doi.org/10.1063/1.1519950http://dx.doi.org/10.1063/1.2815674http://dx.doi.org/10.1063/1.3293295http://dx.doi.org/10.1063/1.3675879http://dx.doi.org/10.1088/0963-0252/21/3/035003http://dx.doi.org/10.1063/1.4770312http://dx.doi.org/10.1063/1.361152http://dx.doi.org/10.1088/0022-3727/38/18/022http://dx.doi.org/10.1088/0022-3727/41/6/065207http://dx.doi.org/10.1063/1.3572264http://dx.doi.org/10.1116/1.1349728http://dx.doi.org/10.1116/1.1642638http://dx.doi.org/10.1063/1.3519515http://dx.doi.org/10.1063/1.3519515http://dx.doi.org/10.1088/0022-3727/45/48/485204http://dx.doi.org/10.1088/0963-0252/19/4/045023http://dx.doi.org/10.1088/0963-0252/20/3/035013http://dx.doi.org/10.1088/0963-0252/20/3/035013http://dx.doi.org/10.1063/1.3112009http://dx.doi.org/10.1063/1.3566007http://dx.doi.org/10.1063/1.363169http://dx.doi.org/10.1116/1.587101http://dx.doi.org/10.1109/27.16552http://dx.doi.org/10.1103/PhysRevA.42.2299http://dx.doi.org/10.1063/1.364199http://dx.doi.org/10.1063/1.365732http://dx.doi.org/10.1063/1.369701http://dx.doi.org/10.1063/1.371446http://dx.doi.org/10.1063/1.372966http://dx.doi.org/10.1103/PhysRevE.65.036403http://dx.doi.org/10.1063/1.1696957http://www.lxcat.laplace.univ-tlse.fr/http://www.lxcat.laplace.univ-tlse.fr/http://dx.doi.org/10.1103/PhysRevA.15.517http://dx.doi.org/10.1063/1.3261836http://dx.doi.org/10.1063/1.352926

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